Lithium secondary batteries are becoming more and more important as power supplies loaded on vehicles or power sources fix PCs, mobile devices, and so on. In particular, lithium-ion secondary batteries, which are lightweight, yet provide high energy densities, are expected as preferable high-power batteries for vehicles. A typical example of a positive electrode active material used in lithium secondary batteries is a composite oxide containing lithium (Li) and at least one transition metal (which may also be referred to as a lithium transition metal oxide, hereinafter). Technical literature relating to lithium secondary batteries includes Patent Documents 1 to 3.